ar

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2sin^2(x)-2cos^2(x)=0

الحلّ

2 sin^{2} (x) - 2 cos^{2} (x) = 0

الحلّ

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

+1

درجات

x = 13 5^{\circ} + 18 0^{\circ} n, x = 4 5^{\circ} + 18 0^{\circ} n

خطوات الحلّ

2 sin^{2} (x) - 2 cos^{2} (x) = 0

2 sin^{2} (x) - 2 cos^{2} (x)

حلل إلى عوامل:

2 (sin (x) + cos (x)) (sin (x) - cos (x))

2 sin^{2} (x) - 2 cos^{2} (x)

2

قم باخراج العامل المشترك

= 2 (sin^{2} (x) - cos^{2} (x))

sin^{2} (x) - cos^{2} (x)

حلل إلى عوامل:

(sin (x) + cos (x)) (sin (x) - cos (x))

sin^{2} (x) - cos^{2} (x)

x^{2} - y^{2} = (x + y) (x - y)

فعّل قانون فرق المربّعات

sin^{2} (x) - cos^{2} (x) = (sin (x) + cos (x)) (sin (x) - cos (x))

= (sin (x) + cos (x)) (sin (x) - cos (x))

= 2 (sin (x) + cos (x)) (sin (x) - cos (x))

2 (sin (x) + cos (x)) (sin (x) - cos (x)) = 0

حلّ كل جزء على حدة

sin (x) + cos (x) = 0 or sin (x) - cos (x) = 0

sin (x) + cos (x) = 0 : x = \frac{3 π}{4} + πn

sin (x) + cos (x) = 0

Rewrite using trig identities

sin (x) + cos (x) = 0

cos (x) \neq = 0, cos (x)

اقسم الطرفين على

\frac{sin ( x ) + cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

بسّط

\frac{sin ( x )}{cos ( x )} + 1 = 0

\frac{sin ( x )}{cos ( x )} = tan (x)

:Use the basic trigonometric identity

tan (x) + 1 = 0

tan (x) + 1 = 0

انقل

1

إلى الجانب الأيمن

tan (x) + 1 = 0

من الطرفين

1

اطرح

tan (x) + 1 - 1 = 0 - 1

بسّط

tan (x) = - 1

tan (x) = - 1

tan (x) = - 1 :

حلول عامّة لـ

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

sin (x) - cos (x) = 0 : x = \frac{π}{4} + πn

sin (x) - cos (x) = 0

Rewrite using trig identities

sin (x) - cos (x) = 0

cos (x) \neq = 0, cos (x)

اقسم الطرفين على

\frac{sin ( x ) - cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

بسّط

\frac{sin ( x )}{cos ( x )} - 1 = 0

\frac{sin ( x )}{cos ( x )} = tan (x)

:Use the basic trigonometric identity

tan (x) - 1 = 0

tan (x) - 1 = 0

انقل

1

إلى الجانب الأيمن

tan (x) - 1 = 0

للطرفين

1

أضف

tan (x) - 1 + 1 = 0 + 1

بسّط

tan (x) = 1

tan (x) = 1

tan (x) = 1 :

حلول عامّة لـ

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

وحّد الحلول

x = \frac{3 π}{4} + πn, x = \frac{π}{4} + πn

أمثلة شائعة

sin^2(x)+2cos^2(x)=2

sin^{2} (x) + 2 cos^{2} (x) = 2

solvefor x,cos^2(x)+cos^2(y)cos^2(z)=1 solve for

x, cos^{2} (x) + cos^{2} (y) cos^{2} (z) = 1

cos(5x)+cos(x)=0

cos (5 x) + cos (x) = 0

solvefor x,f=cos^2(x)solve for

x, f = cos^{2} (x)

cos^2(x)-2cos(x)=-1

cos^{2} (x) - 2 cos (x) = - 1